ONE WAY ANOVA

ONE WAY ANOVA

The one-way analysis of variance (ANOVA) is used to determine whether there is any significant difference between the means of a dependent variable for three or more unrelated groups of an independent variable. One-way ANOVA is particularly used when there is only one independent variable and one dependent variable. The dependent variable is metric (interval or ratio scale) whereas the independent variable is categorical or nominal in nature.

PROBLEM

A manager of XYZ electric bulbs Company wants to compare the life span of three different brands of bulbs available in the market. The manger collected the data of life span of the bulbs of brands A, B and C measured in hundreds of hours during three months period as shown below.

Table-1: Sample Data

The purpose is test whether the lifetimes of four brands of electric bulbs are equal or not.

The hypotheses for the analysis are:

Null hypothesis-H0: The mean lifetimes for three brands of bulbs are equal.

Alternative Hypothesis- H1: The mean life time of at least two brands of bulbs differ.

Input Data

The variable ‘life time’ is dependent variable and the variable ‘brand’ is independent variable. The independent variable is coded as: 1 = Brand A, 2 = Brand B, 3 = Brand C.  The following table depicts the dependent variable along with the coded independent variable and it is treated as the input data matrix for the analysis.

Table-2: Input Data

Performing the Analysis with SPSS

For SPSS Version 11, click on Analyze ⇒ Compare Means ⇒ One-way ANOVA

This will bring up the SPSS screen dialogue box as shown below.

After clicking One-Way ANOVA, this will bring up the following SPSS screen dialogue box

Select the dependent variable and move it to the Dependent list box. Similarly select the coded variable and move it to Factor box.

Now, click OK to get the output.

SPSS Output

The SPSS output of the analysis is given in the following table.

Table-3: ANOVA

From the output, F = 1.473

DECISION

Reject the null hypothesis if p-value (Sig. value) ≤ 0.05

INTERPRETATION

The p-value is 0.302 and it is less than 0.05 (5% level of significance), so we reject the null hypothesis and accept the alternative hypothesis at 5% level of significance. It can be concluded that the life span of different brands of bulbs differ significantly.

CASE ANALYSIS-2

PROBLEM

A pen manufacturing unit is interested to compare the average sales of its four salesmen X, Y, Z and W. The following depicts the weekly sales by the salesmen in hundreds of units.

Table-1: Sample Data

The purpose is test whether the lifetimes of four brands of electric bulbs are equal or not.

The hypotheses for the analysis are:

Null hypothesis-H0: The average sales by three salesmen are equal.

Alternative Hypothesis- H1: The average sales of at least two salesmen differ.

Input Data

The variable ‘sales’ is dependent variable and the variable ‘salesmen’ is independent variable. The independent variable is coded as: 1 = Salesman X, 2 = Salesman Y, 3 = Salesman Z, 4 = Salesman W. The following table is used as the input data for the analysis.

Table-2: Input Data

SPSS Output

The SPSS output of the analysis is given in the following table.

Table-3: ANOVA

From the output, F = 0.392

DECISION

Reject the null hypothesis if p-value (Sig. value) ≤ 0.05

INTERPRETATION

The p-value is 0.762 and it is more than 0.05 (5% level of significance), so we accept the null hypothesis and conclude that the average sales by the salesmen do not differ significantly.

SPSS Command

1. Click on ANALYZE at the SPSS menu bar (in older versions of SPSS, click on STATISTICS instead of ANALYZE).
2. Click on COMPARE MEANS followed by ONE WAY ANOVA.
3. Select the appropriate variable and move it to the DEPENDENT LIST. Similarly select the CODED variable and move it to FACTOR BOX.
4. Click OK to get the output.

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